Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,100 and $14,500.
- Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
- Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
- What amount should you bid to maximize the probability that you get the property (in dollars)?
- Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,050. If your objective is to maximize the expected profit, what is your bid?